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### Catalan's conjecture

The Catalan conjecture states that apart from the powers 2^{3} = 8 and 3^{2} = 9 there are no other *real* powers that differ by exactly 1.

##### Explanation

The conjecture was formulated in 1844 by the Belgian mathematician Eugène Charles Catalan. The calculation can be written as

3

^{2}− 2^{3}= 9 − 8 = 1

##### Additional information

In 2002 the Romanian mathematician Preda Mihăilescu proved that the only solution of two consecutive powers in the natural numbers for

x−^{a}y= 1^{b}

with *x, y, a, b* > 1 actually is *x* = 3, *a* = 2, *y* = 2 and *b* = 3. That is why it is now also called the theorem of Mihăilescu.